Nonlinear Parameter Identification of a Resonant Electrostatic MEMS Actuator

Al‐Ghamdi, Majed; Alneamy, Ayman M.; Park, Sangtak; Li, Beichen; Khater, Mahmoud; Abdel‐Rahman, Eihab; Heppler, G. R.; Yavuz, Mustafa

doi:10.3390/s17051121

Cited by 16 publications

(6 citation statements)

References 20 publications

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“…Najar et al [15] investigated same electrostatically actuated MEMS bridge resonators under same conditions; they reported only the frequency-amplitude response. Lumped models of such structures have been reported by Al-Ghamdi et al [18] and Alsaleem et al [19].…”

Section: Introductionmentioning

confidence: 86%

Voltage–Amplitude Response of Superharmonic Resonance of Second Order of Electrostatically Actuated MEMS Cantilever Resonators

Caruntu

Botello

Reyes

et al. 2019

Journal of Computational and Nonlinear Dynamics

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This paper investigates the voltage-amplitude response of superharmonic resonance of second order (order two) of alternating current (AC) electrostatically actuated microelectromechanical system (MEMS) cantilever resonators. The resonators consist of a cantilever parallel to a ground plate and under voltage that produces hard excitations. AC frequency is near one-fourth of the natural frequency of the cantilever. The electrostatic force includes fringe effect. Two kinds of models, namely reduced-order models (ROMs), and boundary value problem (BVP) model, are developed. Methods used to solve these models are (1) method of multiple scales (MMS) for ROM using one mode of vibration, (2) continuation and bifurcation analysis for ROMs with several modes of vibration, (3) numerical integration for ROM with several modes of vibration, and (4) numerical integration for BVP model. The voltage-amplitude response shows a softening effect and three saddle-node bifurcation points. The first two bifurcation points occur at low voltage and amplitudes of 0.2 and 0.56 of the gap. The third bifurcation point occurs at higher voltage, called pull-in voltage, and amplitude of 0.44 of the gap. Pull-in occurs, (1) for voltage larger than the pull-in voltage regardless of the initial amplitude and (2) for voltage values lower than the pull-in voltage and large initial amplitudes. Pull-in does not occur at relatively small voltages and small initial amplitudes. First two bifurcation points vanish as damping increases. All bifurcation points are shifted to lower voltages as fringe increases. Pull-in voltage is not affected by the damping or detuning frequency.Keywords: superharmonic resonance of the second order, MEMS cantilever resonator, electrostatic actuation, voltage-amplitude response, method of multiple scales (MMS), reduced-order model (ROM), boundary value problem (BVP), fringe effect

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Section: Introductionmentioning

confidence: 86%

Voltage–Amplitude Response of Superharmonic Resonance of Second Order of Electrostatically Actuated MEMS Cantilever Resonators

Caruntu

Botello

Reyes

et al. 2019

Journal of Computational and Nonlinear Dynamics

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“…In addition, the oscillation phenomenon caused by the small damping coefficient and the large spring coefficient of the flexural mechanism is particularly obvious [2]. More than that, the electromagnetic micromirror is also affected by process noise and measurement noise [23][24][25].…”

Section: Dynamic Property and Model Establishment 21 Basic Dynamic Pe...mentioning

confidence: 99%

Online Optimization Method for Nonlinear Model-Predictive Control in Angular Tracking for MEMS Micromirror

Cao

Tan

2022

Micromachines

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In this brief, a precise angular tracking control strategy using nonlinear predictive optimization control (POC) approach is address. In order to deal with the model uncertainty and noise interference, a online Hammerstein-model-based POC is designed using online estimated parameters and model residual. Above all, a rate-dependent Duhem model is used to describe the nonlinear sub-model of the whole Hammerstein architecture for depicting multi-valued mapping nonlinear characteristic. Then, predictive output of angular deflection is obtained by Diophantine function based on linear submodel. Subsequently, the iterative control value depends on estimated parameters through data-driven is acquired. Later, based on the cost function, the iteratively optimization control quantity is fed back to the electromagnetic driven deflection micromirror (EDDM) system on the basis of Hammerstein architecture. It should be stressed that the control value is determined by real-time update model residual and defined cost function. Moreover, the stability of POC strategy is proposed. In addition, experimental result is proposed to validate the effectiveness of the control technique adopted in this paper.

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“…The fundamental natural frequency (f in ) was used to estimate the beam dimensions as-fabricated. This parameter identification technique [28] arrived at identical dimensions except for the structural layer thickness, the beam initial rise and electrostatic gap estimated as h b = 1.9 µm, h • = 2.9 µm and d = 8 µm, respectively. The differences between the designed and fabricated values are within the fabrication process uncertainty limits.…”

Section: Actuator Imentioning

confidence: 99%

Large oscillation of electrostatically actuated curved beams

Alneamy

Khater

Al‐Ghamdi

et al. 2020

J. Micromech. Microeng.

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This paper investigates the responses of initially curved micro-beams subjected to an electrostatic excitation. A Euler–Bernoulli beam theory is utilized to derive the governing equation of motion. A reduced-order model was developed by discretizing the equation of motion using straight beam mode shapes as basis functions in a Galerkin expansion. The results show evidence of the superharmonic resonances of order-three and two in addition to primary resonance. The co-existence of multiple stable orbits observed around only one stable equilibrium and under excitation waveforms with RMS voltage less than the snap-back voltage. These branches are a branch of small orbits within a narrow potential well and two branches of medium-sized and large orbits within a wider potential well. The transition between them results in the characteristic of the double peaks appearing in the frequency-response curve. We also report a bubble structure along the medium-sized branch consists of a cascade of period-doubling bifurcations and a cascade of reverse period-doubling bifurcations. A chaotic attractor develops within that structure at larger excitation levels. It demonstrates evidence of chaos with a wide-based spectrum and an elevated noise-floor. Odd-periodic windows appear also within the attractor including period-three (P-3), period-five (P-5) and period-six (P-6) windows. The chaotic attractor terminates in a cascade of reverse period-doubling bifurcations of period-four (P-4) orbits and period-two (P-2) orbits.

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Nonlinear Parameter Identification of a Resonant Electrostatic MEMS Actuator

Cited by 16 publications

References 20 publications

Voltage–Amplitude Response of Superharmonic Resonance of Second Order of Electrostatically Actuated MEMS Cantilever Resonators

Voltage–Amplitude Response of Superharmonic Resonance of Second Order of Electrostatically Actuated MEMS Cantilever Resonators

Online Optimization Method for Nonlinear Model-Predictive Control in Angular Tracking for MEMS Micromirror

Large oscillation of electrostatically actuated curved beams

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